1÷2(6+4x)-1÷4(8x-12=1÷2(2×-4)
I shall balance your parentheses and assume you meant
1÷2(6+4x)-1÷4(8x-12)=1÷2(2×-4)
That still looks odd, since you appear to have both "x" as a variable and "×" as a multiplication operator. I shall also assume that "×" means the variable "x", based on the overall syntax. That gives us the equation, using some extra spaces to aid in what I hope is clarity,
1÷2(6+4x) - 1÷4(8x-12) = 1÷2(2x-4)
or
1÷4(2x+3) - 1÷16(2x-3) = 1÷4(x-2)
Now, if we multiply through by the LCD to get rid of the fractions, we have
4(2x-3)(x-2) - (2x+3)(x-2) = 4(2x+3)(4x-3)
Now, expanding all that out and collecting terms, you end up with
6x^2-27x+30 = 32x^2+24x-36
26x^2+51x-66 = 0
Now just crank out the quadratic formula to get
x = (-51±√9465)/52
That seems unusually messy, so I may have made some incorrect assumptions. If so, then I'm sure you can fix things up.
I see a typo. Let's proceed from
4(2x-3)(x-2) - (2x+3)(x-2) = 4(2x+3)(2x-3)
6x^2-27x+30 = 16x^2-36
10x^2+27x-66 = 0
x = (-27±√3369)/20
Not much better.
1 + 2(6 + 4x) - 1 + 4(8x - 12) = 1 + 2(2x - 4).
Remove all parentheses by multiplying by the no. outside of it:
1 + 12 + 8x - 1 + 32x - 48 = 1 + 4x - 8,
Combine like-terms:
40x - 36 = 4x - 7,
36x = 29,
X = 29/36.
To solve this equation, we'll follow the order of operations (also known as PEMDAS).
First, let's simplify the expression on both sides of the equation step by step:
1÷2(6+4x) - 1÷4(8x-12) = 1÷2(2×-4)
Step 1: Simplify the parentheses.
Inside the first set of parentheses, we have 6+4x. Inside the second set of parentheses, we have 8x-12.
1÷2(10x) - 1÷4(8x-12) = 1÷2(2×-4)
Step 2: Multiply the coefficient outside the first set of parentheses (1/2) by the expression inside.
(1/2)*(10+4x) - 1÷4(8x-12) = 1÷2(2×-4)
Step 3: Multiply the coefficient outside the second set of parentheses (1/4) by the expression inside.
(1/2)*(10+4x) - (1/4)*(8x-12) = 1÷2(2×-4)
Step 4: Simplify the expressions further.
(10/2 + 4x/2) - (8x/4 - 12/4) = 1÷2(2×-4)
Step 5: Simplify further.
(5 + 2x) - (2x - 3) = 1÷2(2×-4)
Step 6: Remove the parentheses by distributing the division on the right side.
(5 + 2x) - (2x - 3) = (-4)
Step 7: Simplify further.
5 + 2x - 2x + 3 = -4
Step 8: Combine like terms.
8 = -4
At this point, we have reached an inconsistency: 8 is not equal to -4. Therefore, the original equation does not have a solution.